An evaluation method of time history earthquake responses for the shear and drift of each frame in a multi-story asymmetric building is proposed to improve the seismic evaluation method of the Calculation of Response and Limit Strength. Both the time history earthquake response analysis and the modal adaptive pushover analysis, which is a static analysis, for a four-story reinforced concrete asymmetric building are conducted to reduce the building to two kinds of the single degree of freedom systems, the dynamic reduction system and the static reduction system. Using the responses of the dynamic reduction system, the first mode components of the shear and drift responses of each frame are evaluated. The higher mode components of the responses are also evaluated by the proposed method. The validity of the proposed method is demonstrated through comparing the predicted responses with the time history responses analyzed.